Definitenes Effect with haber-sentences

It is well known that existencial sentences with haber are subject to some form of Definiteness Effect DE--as English existentials are (Milsark 1974). But in Spanish this only affects +specific and +animate objects:

(1) *Hay Juan
(2) *Hay el policía de siempre
(3) Hay el problema de siempre

Suñer 1982 noted this, although she tried to use it to deny the DE. I wrote a paper about this and other related issues with haber. Some issues remain, however.

An interesting question is that this restriction is preserved with non-restrictive relative clauses (I know no analysis of this):

(4) * Juan, quien hay en la oficina
(5) * El estudiante, quien hay en la oficina

But restrictive clauses accept this:

(6) El estudiante que hay en la oficina

Some ideas about what is going on?